We present a new algorithm for computing a SAGBI basis up to an arbitrary degree for a subalgebra generated by a set of homogeneous polynomials. Our idea is based on linear algebra methods which cause a low level of complexity and computational cost. We then use it to solve the membership problem in subalgebras.

In this study, the tests of statistical hypotheses with crisp data using small samples are extended to membership function and non-membership intuitionistic fuzzy set. The test procedure for means two normally distributed populations respect any set is proposed.

This paper presents a new adaptive soft combiner implemented on cognitive radio nodes for distributed cooperative spectrum sensing. The key feature of the proposal is the use of the standard set-membership normalized least-mean squares (SMNLMS) algorithm, which enjoys good tracking capabilities, while entailing low computational burden. Indeed, simulation results show that the computational sav...

In previous work, we showed the importance of distinguishing “I know that X = Y ” from “I don’t know that X = Y ”. In this paper we look at effective set membership, starting with Gröbner bases, where the issues are well-expressed in algebra systems, and going on to integration and other questions of ‘computer calculus’. In particular, we claim that a better recognition of the role of set membe...

We logically model uncertainty by expanding language without changing logical reasoning rules. We expand the language of set theory by adding new predicate symbols, uncertain membership relations ∈+ and ∈−. We define the set theory ZF± as an extension of ZF with new symbols in classical logic. In this system we can represent uncertainty which is naturally represented in the model of 3-valued lo...

In this paper a support vector machine (SVM) approach for characterizing the feasible parameter set (FPS) in non-linear set-membership estimation problems is presented. It iteratively solves a regression problem from which an approximation of the boundary of the FPS can be determined. To guarantee convergence to the boundary the procedure includes a no-derivative line search and for an appropri...

In the paper a Nonlinear Set Membership (NSM) prediction method is applied to forecast tropospheric pollution. The NSM method does not require the choice of the functional form of the model used for prediction but only assumes a regularity condition on the regression function defining the model. In this way, the complexity/accuracy problems deriving from the proper choice of a suitable parametr...

This paper deals with adaptive solutions to the socalled set-membership filtering (SMF) problem. The SMF methodology involves designing filters by imposing a deterministic constraint on the output error sequence. A set-membership decision feedback equalizer (SM-DFE) for equalization of a communications channel is derived, and connections with the minimum mean square error (MMSE) DFE are establi...

Set-membership (SM) adaptive filtering is appealing in many practical situations, particularly those with inherent power and computational constraints. The main feature of the SM algorithms is their data-selective coefficient update leading to lower computational complexity and power consumption. The set-membership affine projection (SM-AP) algorithm does not trade convergence speed with misadj...

AbsrractConventional fuzzy logic controller uses input membership functions that consist of identical triangular input membership functions (MF) for all the subsets that are not located at the two ends of the universal set (center width constant or CWC). Some researchers in the field of motor controllers have started using narrower base triangular membership functions for the input subsets that...